Numerical and Experimental Evaluation of Error Estimation for Two-Way Ranging Methods

Article

Numerical and Experimental Evaluation of Error Estimation for Two-Way Ranging Methods ^†

Cung Lian Sang * , Michael Adams, Timm Hörmann, Marc Hesse , Mario Porrmann and Ulrich Rückert

Cognitronics and Sensor Systems Group (CITEC), Bielefeld University, 33619 Bielefeld, Germany;

madams@techfak.uni-bielefeld.de (M.A.); thoerman@techfak.uni-bielefeld.de (T.H.);

mhesse@techfak.uni-bielefeld.de (M.H.); mporrman@techfak.uni-bielefeld.de (M.P.);

rueckert@techfak.uni-bielefeld.de (U.R.)

* Correspondence: csang@techfak.uni-bielefeld.de; Tel.: +49-521-106-67368

† This paper is an extended version of our paper published in “C. Lian Sang, M. Adams, T. Hörmann, M. Hesse, M. Porrman, U. Rückert. An Analytical Study of Time of Flight Error Estimation in Two-Way Ranging Methods. In Proceedings of the 2018 International Conference on Indoor Positioning and Indoor Navigation (IPIN), Nantes, France, 24–27 September 2018, doi:10.4119/unibi/2919795”.

Received: 31 December 2018; Accepted: 29 January 2019; Published: 1 February 2019 Abstract: The Two-Way Ranging (TWR) method is commonly used for measuring the distance between two wireless transceiver nodes, especially when clock synchronization between the two nodes is not available. For modeling the time-of-flight (TOF) error between two wireless transceiver nodes in TWR, the existing error model, described in the IEEE 802.15.4-2011 standard, is solely based on clock drift. However, it is inadequate for in-depth comparative analysis between different TWR methods. In this paper, we propose a novel TOF Error Estimation Model (TEEM) for TWR methods. Using the proposed model, we evaluate the comparative analysis between different TWR methods. The analytical results were validated with both numerical simulation and experimental results. Moreover, we demonstrate the pitfalls of the symmetric double-sided TWR (SDS-TWR) method, which is the most highlighted TWR method in the literature because of its highly accurate performance on clock-drift error reduction when reply times are symmetric. We argue that alternative double-sided TWR (AltDS-TWR) outperforms SDS-TWR. The argument was verified with both numerical simulation and experimental evaluation results.

Keywords:TEEM; TWR; AltDS-TWR; SDS-TWR; distance measurement; error analysis; delay effects;

TOF error model

1. Introduction

The field of localization systems in wireless communications is growing since it enables a wireless mobile node to have both data communication and positioning capabilities. The localization process is typically categorized into two phases: (i) ranging (measurement) phase, during which the distance between the transceivers is measured, and (ii) positioning (location-update) phase, during which the current position of the wireless node is determined using the knowledge from the ranging phase and positioning algorithms [1]. Regarding positioning, besides wireless-only positioning systems, multiple sensor approaches, like diversity navigation, have been proposed as well [1]. In those systems, ranging is supported by using additional information, e.g., from an Inertial Measurement Unit (IMU). In this paper, we focus on the accuracy of wireless ranging based on Ultrawide Bandwidth (UWB), and specifically study different Two-Way Ranging (TWR) methods available in the literature.

TWR plays an important role in measuring the distance between two wireless transceiver devices when clock synchronization is not available or absent in a time-based localization system. By knowing

Sensors2019,19, 616; doi:10.3390/s19030616 www.mdpi.com/journal/sensors

the Time of Flight (TOF) between the two transceivers, i.e., a signal’s traveling time in free space, the distance between them can easily be measured using the speed of light. However, it is necessary that the two transceivers have a synchronized clock (same clock domain) in such one-way ranging systems.

In the TWR approach, a set of time periods (e.g., tround = 10 µs andtreply = 4 µs) is used to calculate the distance between two transceivers (Section2) instead of using direct timestamps. This is because the period of a certain time is the same for every device regardless of their own clock references.

However, because of the imperfections of clock oscillators in the real physical world, a clock drifts away even if it is perfectly tuned in the initial state [2]. These clock drifts cause inaccuracy in measuring the mentioned time periods, especially when the application requires centimeter-level accuracy. This is because 1 ns of TOF error can lead to an approximate error of 30 cm in distance estimation [3]. For this reason, there are several TWR methods available in the literature to minimize this inaccuracy in ranging due to clock drifts (Section2).

As a consequence, the existing TOF error-estimation model for TWR, described in the IEEE 802.15.4-2011 standard, tackles clock drifts as the only dominant errors [3] (pp. 258–275). However, this model is inadequate for analysis of system performance between different TWR methods, especially when it is important to identify a better method for a certain application. For instance, the performance difference between two closely related TWRs, such as a symmetric double-sided TWR (SDS-TWR) and alternative double-sided TWR (AltDS-TWR), cannot be definitely clarified using the existing model [4].

Moreover, AltDS-TWR is robust against the variation of reply time, as we discuss in Section7.3.1, which cannot be explained with a conventional clock-drift model, as above.

In this paper, we propose a novel Time-of-Flight Error Estimation Model (TEEM) for TWR methods, which is an extended version of the IEEE 802.15.4-2011 standard [3] (pp. 258–275).

Regarding this, a delay in message delivery (Section3.1) is accounted as a feature in the proposed model. In fact, this delay is crucial and fundamental, because TOF error is affected not only by clock drift in the oscillator but also by other error sources, such as propagation time delay [5], transmission time delay, and receiving time delay [2]. That includes the delay introduced by the antenna, PCB, and other external and internal electronic components.

In addition, we demonstrate the pitfalls of the most highlighted TWR techniques in the literature, namely, SDS-TWR. Conventionally, SDS-TWR is commonly used to illustrate the reduction of TOF error due to clock drifts in wireless ranging systems [3]. Concerning this, we argue that AltDS-TWR is more robust than SDS-TWR in all aspects.

This article is the extended version of our previous conference paper, presented in IPIN 2018 [6].

Three significant changes were made. Firstly, experiment results for different TWR methods are given to validate the simulation results presented in the conference paper (Section7). Secondly, we provide the generic delay model for TWR methods (Sections3.1and3.2), which was regarded as a propagation time-delay error in our previous work [6]. Thirdly, we verify our argument, which is that AltDS-TWR method outperforms SDS-TWR, with both numerical simulation (Section6) and experimental evaluation (Section7) results.

This paper is organized as follows: In Section2, the overview of TWR methods, the existing standard TOF error-estimation approach, and related work are addressed. Then, the foundation of the proposed TOF error-estimation model is established in Section3, followed by analytical comparison between the proposed and conventional TOF error estimation in Section4. A comparative study between four TWR methods using the proposed model is provided in Section5, and the numerical simulation results are presented in Section6. Then, the experimental evaluation results are given in Section7, and a summarized discussion in Section8. Final conclusions are drawn in Section9.

2. State of the Art for TWR Methods and Related Work

In this section, we address four commonly used TWR methods in time-based wireless localization systems and the existing TOF error-estimation model, given in the IEEE 802.15.4-2011 standard.

IEEE 802.15.4 uses clock drifts as the only dominant error to compare TOF errors among different TWR methods [3].

Brief introductions for each of the evaluated TWR methods, which are the single-sided TWR (SS-TWR), (symmetric) DS-TWR, AltDS-TWR, and asymmetric double-sided TWR (ADS-TWR), are presented in this section. These methods were carefully chosen to reflect the general overview of the available TWR methods in the literature. The remaining TWR methods, derived mainly from the presented techniques, are: SDS-TWR with multiple acknowledgments [7], asynchronous double TWR (D-TWR) [8], burst-mode SDS-TWR [9], SDS-TWR with unequal reply-time method [10], TWR using estimated frequency offsets [11], parallel DS-TWR [12], and passive extended DS-TWR [13].

Apart from measuring distances between transceivers in wireless communications, TWR has also been widely applied in networkwide clock-synchronization algorithms for wireless sensor networks (WSN) [14–17].

2.1. (Simple) SS-TWR

For SS-TWR [3,18] (the shaded area in Figure 1), the round-trip time of the signal can be formulated as:

t_roundA =₂T_{to f} +t_replyB (1)

where t_roundA = τ_ARx−τ_ATx is the true round-trip time of a signal measured at Device A and t_replyB = τBTx−τBRx is the true reply time of a signal measured at Device B (Figure1). τ_ATx and τ_ARx are the transmitted and received timestamps measured at Device A, andτ_BTxandτ_BRxare the transmitted and received timestamps measured at Device B, respectively.

In particular, the round-trip time of a signal (t_roundA) is measured from the beginning of Device A transmitting the ranging message (τ_ATxin Figure1) until the reception of the replied signal back from Device B (τARx in Figure1). Therefore, the TOF for the SS-TWR method can be obtained as:

Tto f = ¹

2(troundA−treplyB) (2)

Device A Device B

t_roundA

t_roundB

t_replyB

t_replyA T_tof

T_tof

T_tof τ_ATx

τ_ARx

τBRx

τ_BTx DS- SS-

Figure 1.Illustration of single- and double-sided Two-Way Ranging (TWR) methods ( c2018 IEEE.

Reprinted with permission).

2.2. SDS-TWR

The round-trip time of double-sided TWR [3,18] (Figure1) can be formulated as:

t_roundA =2T_{to f} +t_replyB (3a)

t_roundB =₂T_{to f} +t_replyA (3b)

where t_roundA andt_roundB are the true round-trip times of a signal measured at Device A and B, respectively.t_replyAandt_replyBare the true reply times measured at Device A and B, respectively.

By combining Equations (3a) and (3b), the resulting TOF for SDS-TWR or DS-TWR can be expressed as:

T_{to f} = ¹

4((t_roundA−t_replyA) + (t_roundB−t_replyB)) (4) In DS-TWR, the ranging time for a single measurement is approximately less than twice as long as SS-TWR due to the additional reply time, as depicted in Figure1.

2.3. AltDS-TWR

The AltDS-TWR method [4] shares the same core concept as Equations (3a) and (3b) from Section2.2(Figure1), as follows:

troundA =2Tto f +treplyB (5a)

t_roundB =2T_{to f} +t_replyA (5b)

However, instead of combining the two equations, the AltDS-TWR method is achieved by multiplying Equations (5a) and (5b) as:

t_roundA·t_roundB= (2T_{to f} +t_replyB)·(2T_{to f} +t_replyA) By simplifying the equation, theT_{to f} is obtained as follows:

T_{to f} = ^troundA·t_roundB−t_replyA·t_replyB

troundA+treplyA+troundB+treplyB (6)

The detailed derivation of the formula can be found in Reference [4].

2.4. ADS-TWR

Asymmetric double-sided TWR [19] (Figure2) can be formulated as follows:

t_roundA =2T_{to f} +t_replyB (7a)

t_roundB=₂T_{to f} (7b)

Device A Device B

t_roundA

t_roundB

t_replyB T_tof

T_tof T_tof

Figure 2. Illustration of the asymmetric double-sided TWR method ( c2018 IEEE. Reprinted with permission).

By combining Equations (7a) and (7b), theT_{to f} for ADS-TWR can be achieved as:

T_{to f} = ¹

4(t_roundA+t_roundB−t_replyB) (8)

The major motivation behind the implementation of ADS-TWR is to reduce the ranging time of the system while attaining the same performance level as SDS-TWR or AltDS-TWR.

2.5. Conventional TOF Error Estimation Approaches

The existing conventional TOF error-estimation approach, i.e., the IEEE 802.15.4-2011 standard [3] (pp. 258–275), is specifically only based on clock-drift error effects in TWR methods.

The fundamental model can be simplified as in the following equations according to the method originally proposed in Reference [18] and presented in Reference [3]. Then, the method was later extensively applied and studied in References [4,8,9,19,20]. The corresponding concept is depicted in Figure1. The representation of the equations is inspired by the work in Reference [4].

tˆ_roundA= (₁+e_A)t_roundA (9a)

tˆreplyA= (1+eA)treplyA (9b)

tˆ_roundB = (1+eB)t_roundB (9c)

ˆt_replyB= (₁+e_B)t_replyB (9d)

where ˆt_roundAand ˆt_roundBare the estimated round-trip times of Devices A and B, respectively.t_roundA andt_roundBare the true round-trip times of Devices A and B, respectively. ˆt_replyAand ˆt_replyBare the estimated replied times of Devices A and B, respectively.t_replyA andt_replyBare the true replied times of Devices A and B, respectively.eAandeBare the clock-drift errors introduced by Devices A and B, respectively. It is conventionally assumed thatT_{to f} <<t_replyAort_replyB. The reason is that reply times are in the order of several milliseconds, whileT_{to f} is in the order of nanoseconds [3].

Moreover, a linear algebra approach on error analysis of a co-operative position system using GPS and TWR was performed in Reference [21]. The overall concept is interesting because the presented method can be used as a transition system that bridges the localization systems of UWB (indoor) and GPS (outdoor). However, error analysis performed for TWR in the work is too shallow. The authors assumed in their work that, firstly, clock-drift errors are compensated just by using the SDS-TWR method, and secondly, ranging measurement error is purely white Gaussian noises. This assumption is too broad to reflect the actual TOF error in the TWR method. In addition, the error model and protocol specifically for the parallel double-sided TWR (PDS-TWR) method were performed in Reference [12].

The authors clearly sketch the source of error in two phases, namely, the ranging and localization processes, and focused on the former phase. Then, the variation of ranging error upon symmetric and quasisymmetric cases are discussed. It was proven in their work that PDS-TWR outperforms SDS-TWR. However, the error term used in their proposed model is unclear, which is defined as the difference between a duration measured with the PHY of a node and real duration (ppm). In addition, the presented error model is not generic and defined only for PDS-TWR method.

3. Proposed Analytical Model

In the following, we outline the problem statement and sketch various error sources (Section3.1).

Subsequently, we describe our extended error model (Section3.2).

3.1. Problem Statement

TWR methods are excellent in ranging distances between two wireless transceiver devices without using clock synchronization. However, clock-drift errors in oscillators (e.g., ±20 ppm in

the IEEE 802.51.4-2011 standard [3]) degrade their performance. The conventional TOF error approach specifically tackles clock drifts as the only dominant error source in TWR methods.

However, the estimation ofTto f in a time-based wireless communication system is fundamentally perturbed by various delay error sources as already mentioned in Section1. These delay sources, especially for time-based localization schemes, can be categorized as follows:

• Propagation-Time Delay (PTD): propagation time is the time required for a message to be transmitted from the transmitter to the receiver in a wireless channel [2]. PTD occurs in two cases: When the direct path signal is completely obstructed or blocked, or when the signal has to traverse through different materials [5]. In other words, PTD occurs when the path of the signal has been reflected or obstructed by obstacles.

• Transmission-Time Delay (TTD): This is the delay caused by the time required for building a message at the application layer (software), accessing time in the medium access control (MAC) layer (protocol), and transmitting time of the message in the physical (PHY) layer [2,14].

This includes delays introduced by the antenna, PCB, and other external and internal electronic components.

• Receiving-Time Delay (RTD): The delay caused by the time required for receiving a message at the PHY, MAC, and application layers, similar to transmission-time delay [2,14].

• Preamble Accumulation-Time Delay (PATD: This is the time required for detecting a certain preamble sequence and finding the start-frame delimiter (SFD) sequence in the PHY layer [22], especially when a coherent receiver [23] is used in the system. PATD is influenced by the presence of a multipath [24] and quick frame arrival time [3] (pp. 261–263) because of a relatively short distance measurement [22] (p. 32). It is more significant when the reflected signal arrives within the chip period of the first path signal [24].

For the sake of simplicity without loss of generality, the mentioned delay errors forT_{to f} estimation in wireless communication systems can be modeled as a simple linear equation. For a single round-trip time in the SS-TWR technique (Figure1), the total round-trip time delay can be formulated as:

∆ABA =

∑

(AB_Delay_i+BA_Delay_i)

≈2·

∑

Delay_i (10)

≈2·(TTD+PTD+PATD+RTD)

where∆ABAis the total delay that occurred within a single round-trip-time of a signal in the TWR method measured at Device A (Figure1). That is, the total delay produced by a signal transmitted from Device A to B and back to Device A. TheDelaycan be one or more of the previously mentioned individual delays, which are TTD, PTD, PATD, and RTD. The total number of delays that could affect the mentioned round-trip delay error in the SS-TWR method is given asn(10). Note that the constant

“2” in Equation (10) appears to represent the two-way traveling routes of a signal in the SS-TWR method for a single measurement. Here, it is assumed that the delays produced in the first route (Device A to B) and the second route (Device B to A) are the same.

Regarding this, the absolute error and relative error for the above-mentioned total delay in the single round-trip-time of TWR (shaded area in Figure1) can be calculated as follows [25] (p. 62):

e=estimated value−exact value=t^ˆ_roundA−t_roundA (11) ξ= absolute error

exact value = ^e troundA

= ^tˆroundA−t_roundA troundA

(12) whereeandξare the absolute error and relative error of the above-mentioned delay (∆ABA).

Assuming that the absolute error is only affected by the above-mentioned delay (∆ABA) in the measurement, the estimated round-trip-time for SS-TWR becomes ˆt_roundA = t_roundA+_∆ABA. By substituting this value into Equation (12), the relative error for the total delay within the single-round-trip time of SS-TWR can be represented as:

ξ_ABA= ^∆ABA

t_roundA (13)

whereξ_ABAis the relative error of the total delay in a single-round-trip time of a signal in SS-TWR method measured at Device A (shaded area in Figure1).

If there is absolutely no delay (∆ABA=0) between the two transceivers in the SS-TWR method, the corresponding relative error upon round-trip time delay (ξ_ABA) equals zero. Otherwise, the round-trip time delay (ξ_ABA) is the relative error achieved from the summation of all related delays along the path. Correspondingly, relative delay errors for the DS-TWR method areξ_BABandξ_ABA.

3.2. Proposed TOF Error-Estimation Model

As it is explained in Section3.1, our proposed model is based on both clock-drift error and the relative error in a round-trip time delay. The analytical formulas for the proposed TOF error-estimation model are provided as follows, in reference to Figure1:

tˆroundA= (1+eA+ξ_ABA)troundA (14a)

tˆ_replyA= (1+eA)t_replyA (14b)

ˆt_roundB= (1+e_B+ξ_BAB)t_roundB (14c)

ˆtreplyB= (1+eB)treplyB (14d)

whereξ_ABAandξ_BAB(as introduced in Section3.1) represent the delay defined as the relative error in the single round-trip time of a signal measured at Device A or B respectively.

Since ξ_ABA and ξ_BAB represent the relative error of the total delay within a single round trip of a TWR system, it is sufficient that their effects are represented in the estimated round-trip time (ˆt_roundAEquation (14a) and ˆt_roundB) alone as provided in Equations (14a) and (14c). Therefore, the estimated reply time (ˆt_replyAand ˆt_replyB) can stay unchanged as in the conventional clock-drift error approach (Section2.5).

It should be noted thatξ_ABAandξ_BABin Equations (14a) and (14c), defined in Section3.1, are completely different parameters from clock-drift errorse_AandeB, which are susceptible to the finite crystal tolerance of the clock oscillators [3].

4. Extended State-of-the-Art TWR Methods

In this section, we compare the proposed and conventional TOF error-estimation models on the evaluated four TWR methods.

4.1. Extended SS-TWR Method

By using Equation (2), the estimated TOF for the SS-TWR method can be written as:

Tˆ_{to f} = ¹

2(t^ˆ_roundA−t^ˆ_replyB) where ˆT_{to f} is the estimated TOF in the system.

The difference between the estimated and true TOF for SS-TWR is:

Tˆto f −Tto f = (t^ˆroundA−t^ˆreplyB)

2 −(troundA−treplyB) 2

By applying Equations (14a) and (14d), the equation becomes:

Tˆ_{to f} −T_{to f} = ¹

2[(e_A+ξ_ABA)t_roundA−eBt_replyB] SubstitutingtroundAwith Equation (1) yields:

Tˆ_{to f} −T_{to f} = ¹

2[2T_{to f}(eA+ξ_ABA) + (eA−eB+ξ_ABA)t_replyB] This leads to the TOF error for SS-TWR as:

Tˆto f−Tto f =Tto f(eA+ξ_ABA) +¹

2(eA−eB)treplyB+¹

2ξ_ABAtreplyB (15)

For the sake of comparison, the TOF error for SS-TWR using the conventional approach from Equations (9a) and (9d) is:

Tˆ_{to f} −T_{to f} =T_{to f}eA+¹

2(eA−eB)t_replyB (16)

It should be noted that our model Equation (15) reduces to conventional Model Equation(16), ifξ_ABA=0.

4.2. Extended SDS-TWR Method

Similar to Section4.1, if Equation (4) is applied in the proposed error model from Equations (14a)–(14d), and by replacingt_roundAandt_roundBwith Equations (3a) and (3b), theTOFerror between the estimated and the true value for SDS-TWR becomes:

Tˆ_{to f}−T_{to f} = ¹

2T_{to f}(e_A+e_B+ξ_BAB+ξ_ABA) +¹

4(e_A−e_B)(t_replyB−t_replyA) +¹

4(ξ_BABt_replyA+ξ_ABAt_replyB) (17)

For the sake of comparison, the conventional model for TOF error in the SDS-TWR method using Equations (9a)–(9d) is:

Tˆ_{to f}−T_{to f} = ¹

2T_{to f}(e_A+e_B) +¹

4(e_A−e_B)(t_replyB−t_replyA) ₍₁₈₎ Again, Equation (17) reduces to (18), if there is no delay in message delivery.

4.3. Extended AltDS-TWR Method

By applying Equation (6) into the proposed error model from Equations (14a)–(14d), and by assumingTto f <<treplyA(or)treplyB(Section5.1), the TOF error between the estimated and the true value for AltDS-TWR becomes:

Tˆ_{to f} −T_{to f} ≈ ^{C1treplyAtreplyB}

C₂t_replyA+C₃t_replyB (19)

whereC1=ξ_BAB(1+eA) +ξ_ABA(1+eB) +ξ_BABξ_ABA,C2=2+eA+eB+ξ_BABandC3 =2+eA+ eB+ξ_ABA. The formula derivation is publicly available in Reference [26].

For the sake of comparison, the TOF error for the AltDS-TWR method [4] using the conventional model from Equations (9a)–(9d) is:

Tˆto f −Tto f =eA·Tto f (or) ˆTto f−Tto f =eB·Tto f (20)

Again, Equation (19) equals zero if it is assumed thatξ_BAB =0 andξ_ABA=0. This explains that the actual TOF error is associated only withT_{to f} as in Equation (20). This is because it is assumed that Tto f is negligible (Tto f <<_{treplyA(or)Tto f} <<_treplyB) when Equation (19) is formulated [26].

4.4. Extended ADS-TWR Method

By substituting Equations (14a), (14c) and (14d) in Equation (8), and by replacing thet_roundAand troundBwith Equations (7a) and (7b), theTOFerror for the ADS-TWR method can be formulated as:

Tˆto f−Tto f = ¹

2Tto f(eA+eB+ξ_ABA+ξ_BAB) +¹

4(eA−eB)treplyB+¹

4(ξ_ABA−ξ_BAB)treplyB (21) For comparison, the TOF error for the ADS-TWR method using the conventional model from Equations (9a), (9c) and (9d) is:

Tˆto f−Tto f = ¹

2Tto f(eA+eB) +¹

4(eA−eB)treplyB (22)

5. Analytical Comparison of TWR Methods

In this section, we compare the analytical results of TOF error among different TWR methods.

To do this, we classify three types of assumptions as defined in Section5.1.

5.1. Error-Model Classification in Three Types

In order to uniformly compare the four evaluated TWR methods, we establish three assumptions (Table1). In each of the three assumptions, it is assumed thatT_{to f} is negligible compared to reply time (t_replyAandt_replyB), i.e.,T_{to f} <<t_reply,t_replyA,t_replyB. Detailed comparison and discussion upon these three assumptions are addressed in Sections5.2–5.4. The three types of assumptions (Table1) are:

Type I Assumption: This is an ideal case. AssumeT_{to f} << t_reply, eA = eB = e = 0, and t_replyA =t_replyB=t_reply. In this assumption, not only are there no clock-drift errors between the two evaluated devices, but reply times are also assumed to be the same.

Type II Assumption: This is a special case. AssumeTto f <<treplyandtreplyA =treplyB=treply. In this assumption, clock-drift error does exist in the evaluated two devices. However, reply times between them are assumed to be the same.

Type III Assumption: This is a typical case. AssumeT_{to f} <<t_replyandt_replyA 6=t_replyB. In this assumption, not only does clock-drift error exist in the evaluated two devices, but also the reply time between them is different.

Table 1.Three assumption types for time-of-flight (TOF) Classification Errors ( c2018 IEEE. Reprinted with permission).

Types Round-Trip Delay Clock Drifts Reply Time Type I ξ=ξ_BAB=ξ_ABA e_A=e_B=0 t_replyA=t_replyB Type II ξ_BAB,ξ_ABA e_A,e_B t_replyA=t_replyB Type III ξ_BAB,ξ_ABA e_A,e_B t_replyA6=t_replyB

5.2. Comparison of TWR Methods in Ideal Cases (Type I)

According to the Type I assumption, we can conclude thatξ_BAB=ξ_ABA=ξ. By applying this ideal assumption to Equations (15), (17), (19) and (21), the TOF error between the estimated and true value among TWR methods can be summarized as follows:

Tˆ_{to f} −T_{to f} ≈ ¹

2ξt_reply (23)

The TOF error for all methods is now approximated as given in Equation (23). The formula derivation for AltDS-TWR is publicly available in Reference [26].

5.3. Comparison of TWR Methods in Special Cases (Type II)

By applying a Type II assumption in Equations (15), (17), (19), and (21), the TOF error between the estimated and true value among TWR methods can be represented as follows:

The SS-TWR method becomes:

Tˆto f −Tto f ≈ ¹

2(eA−eB+ξ_ABA)treply (24)

The SDS-TWR method turns into:

Tˆ_{to f}−T_{to f} ≈ ¹

4(ξ_BAB+ξ_ABA)t_reply (25)

The AltDS-TWR method is:

Tˆto f−Tto f ≈ ^KA

KBtreply (26)

where,K_A = ξ_BAB(1+e_A) +ξ_ABA(1+eB) +ξ_BABξ_ABAandKB = 4+2(e_A+eB) +ξ_BAB+ξ_ABA. The formula derivation is publicly available in Reference [26].

The ADS-TWR method becomes:

Tˆ_{to f} −T_{to f} ≈ ¹

4(e_A−e_B+ξ_ABA−ξ_BAB)t_reply (27)

By comparing Equation (24) to (27), we can conclude that SDS-TWR (25) and AltDS-TWR (26) are superior to SS-TWR (24) and ADS-TWR (27). The reason is that, ifξ_BAB =0 andξ_ABA=0, the TOF error for SDS-TWR (25) and AltDS-TWR (26) is approximately equal to zero.

5.4. Comparison of TWR Methods in Typical Cases (Type III)

By applying a Type III assumption in Equations (15), (17), (19) and (21), the TOF error among the evaluated TWR methods is as follows:

The SS-TWR method becomes:

Tˆto f −Tto f ≈ ¹

2(eA−eB+ξ_ABA)treplyB (28)

The SDS-TWR method turns into:

Tˆto f −Tto f ≈ ¹

4(eA−eB)(treplyB−treplyA) +¹

4(ξ_BABtreplyA+ξ_ABAtreplyB) (29) The AltDS-TWR method is:

Tˆ_{to f} −T_{to f} ≈ ^{C1treplyAtreplyB}

C2treplyA+C3treplyB (30)

whereC1=ξ_BAB(1+eA) +ξ_ABA(1+eB) +ξ_BABξ_ABA,C2=2+eA+eB+ξ_BABandC3 =2+eA+ e_B+ξ_ABA. The formula derivation is available in Reference [26].

The ADS-TWR method becomes:

Tˆto f−Tto f ≈ ¹

4(eA−eB+ξ_ABA−ξ_BAB)treplyB (31) By comparing Equations (28)–(31), we can conclude that the AltDS-TWR Equation (30) method stands out to be the best choice for minimizing TOF error. This is because the TOF error is approximately equal to zero if it is assumed that there are absolutely no delay errors in the message delivery, i.e., ξ_BAB =0 andξ_ABA=0.

6. Numerical Simulation Results

In this section, we present the numerical simulation results of the proposed analytical model given in Section5. Simulations have been performed upon the parameters, which are clock-drift errors eAandeB, the reply time of responder device (treplyAandtreplyB), and the relative delay error in the round-trip time of a signal (ξ_BABandξ_ABA), introduced in Section3.1. The numerical sample values used for the simulations are shown in Table2. The relative delay error in round-trip time for both transceivers is assumed to be the same, i.e.,ξ= ξ_BAB =ξ_ABA, in the presented simulation results.

Moreover, the same random seed value is used foreAandeBthroughout the simulations.

Table 2.Sample Values used in Numerical Simulations ( c2018 IEEE. Reprinted with permission).

Parameters Symbols Range of Value Unit

Relative delay error in round-trip time ξ=ξ_BAB=ξ_ABA 0:0.025:5 ppm Reply times in responder device t_reply=t_replyB 0:5:1000 µs

t_replyA 0 :11:2200 µs

Clock-drift error e_A,e_B ±20 as stated in ppm

(pseudorandom) 802.15.4-2011 [3]

6.1. Simulation Results for Ideal Cases (Type I)

The ideal condition is the simplest and also the reference case because it defines how the system is expected to behave. From Figure3, it is observed that TOF error in an ideal case increases monotonically as both round-trip time delay (ξ) and reply time (t_reply) are increased. Moreover, all TWR methods perform equally well in ideal conditions.

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

Relative Error of Round Trip Time Delay / ppm 10^-6 0 s

0.5 s 1 s 1.5 s 2 s 2.5 s

TOF Error, Type I Assumption / s

10^-9 (b) Type I: SS-,SDS-,ADS, AltDS

t_reply = 50 s t_reply = 400 s treply = 1000 s

Figure 3.TOF error comparison using a Type I assumption (ideal case) as in Equation (23) ( c2018 IEEE. Reprinted, with permission).

6.2. Simulation Results for Special Cases (Type II)

A comparison between the TWR methods for special cases (Type II) is illustrated in Figure4 relative to round-trip time delay (ξ) and reply time (t_reply). Fxed reply timet_reply =490µs is set in the simulation to match the hardware setup in the experimental evaluation (Section7). Interestingly, it is evident that the AltDS-TWR method retains the exact same performance as the SDS-TWR method (Figure4c).

In this special case, both the AltDS-TWR and SDS-TWR method provide numerically stable outputs for TOF error estimation (Figure 4c). In essence, TOF error in all evaluated methods is perpetually increased due to clock drifts as reply time (treply) and round-trip time delay (ξ) are increased (Figure4).

According to the value of parameters used in the simulation (Table2), the TOF error for both the SDS-TWR and AltDS-TWR method is less than 1 ns ifξ<3 ppm andt_reply <650µs. This corresponds to approximately less than 30 cm error in physical-distance measurement. Under the assumption that the round-trip time delay for both transceivers is symmetric, ifξcan be decreased to 2 ppm, then t_replycan be relaxed up to 1 ms without the loss of the above-mentioned accuracy (30 cm). The same principle applies the other way around, too, i.e, decreasingt_replyrelaxes the increase ofξ.

Figure 4. TOF error comparison using a Type II assumption (special case) in accordance with Equations (24)–(27). (a) TOF error for SS-TWR and SDS-TWR on 65 sample points (see Table2);

(b) TOF error vs. delay (ξ); and (c) TOF error specifically for SDS-TWR and AltDS-TWR.

6.3. Simulation Results for Typical Cases (Type III)

The simulation results for a typical condition (Type III) between the four evaluated TWR methods are provided in Figure5. Figure5a compares the performance of the TWR methods when the reply time in Device A (t_replyA = 840 µs) is greater than the reply time in Device B (t_replyB = 400 µs).

In contrast, Figure5b compares the performance of the TWR methods when the two reply times are in the opposite order (treplyA <treplyB) by switching the value of the mentioned reply times. Figure5c–e illustrates the variation of TOF error in SDS-TWR upon different reply times. The reply-time values in the simulation (Figure5) were chosen to match with the hardware setup in the experimental evaluation (Section7).

-6 s -4 s -2 s 0 s 2 s 4 s 6 s 8 s

TOF Error (Type III) / s

10^-9 (a) Type III: t_replyA= 840 s and t_replyB= 400 s

AltDS SDS SS ADS

-1 s -0.5 s 0 s 0.5 s 1 s 1.5 s

2 s 10^-8 (b) Type III: t_replyA= 400 s and t_replyB= 840 s

AltDS SDS SS ADS

-6 s -4 s -2 s 0 s 2 s 4 s 6 s 8 s

TOF Error (Type III) / s

10^-9 (c) Type III: t_replyA= 1140 s and t_replyB= 400 s

AltDS SDS SS ADS

-1 s -0.5 s 0 s 0.5 s

1 s 10^-8 (d) Type III: t_replyA= 1640 s and t_replyB= 400 s

AltDS SDS SS ADS

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

Relative Error of Round Trip Time Delay / ppm 10^-6 -1.5 s

-1 s -0.5 s 0 s 0.5 s 1 s 1.5 s

TOF Error (Type III) / s

10^-8 (e) Type III: t_replyA= 2140 s and t_replyB= 400 s

AltDS SDS SS ADS

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

Relative Error of Round Trip Time Delay / ppm 10^-6 0 s

0.2 s 0.4 s 0.6 s 0.8 s 1 s 1.2 s 1.4 s 1.6 s

1.8 s 10^-9 (f) Type III: Illustration of AltDS-TWR from (a) to (e) scenarios AltDS (840, 400)

AltDS (1140, 400) AltDS (1640, 400) AltDS (2140, 400)

Figure 5.TOF error comparison between TWR methods using Type III assumption (typical case) as in Equations (28)–(31). (a) TOF error whent_replyA > t_replyB, (b) TOF error whent_replyA < t_replyB, (c) TOF error whent_replyA = 1140 µs andt_replyB = 400 µs, (d) TOF error whent_replyA = 1640 µs andt_replyB = 400 µs, (e) TOF error whent_replyA = 2140 µs andt_replyB = 400 µs, and (f) TOF error specifically for AltDS-TWR method at different reply times.

It is evident that the SDS-TWR method suffers severe clock-drift error effects in a typical condition (Type III) when the reply time is asymmetric (Figure5a–e). However, the AltDS-TWR method still holds a numerically stable result in each evaluation (Figure5f).

Note that the ADS-TWR and SS-TWR methods rely solely on one-sided reply time (t_replyB).

Therefore, the duration of t_replyB is crucial for their performance. On the one hand, when treplyB<treplyA, the ADS-TWR method yields a lower TOF error than the SDS-TWR method, while SS-TWR has a fairly comparable result (Figure5a). On the other hand, when t_replyB > t_replyA, the performance of the SS-TWR and ADS-TWR methods degrades, while the performance of the SDS-TWR method is unchanged. In this scenario, the TOF error in the SDS-TWR method is lower than both the SS-TWR and ADS-TWR method (Figure5b). The severity of the TOF error in SDS-TWR increases as the magnitudes of difference between the two reply times increases (Figure5a–e).

7. Experimental Evaluation Results

The experimental evaluations of the three TWR methods, namely, SS-TWR, SDS-TWR, and AltDS-TWR, are conducted in this section. Note that the ADS-TWR method is not included in the experimental evaluation because the hardware used in the experiment doesn’t support the necessary

mechanism for ADS-TWR (Figure2) at the time of our evaluation, which is the instant reply time in Device A (t_replyA=0) or an autoacknowledgment mechanism in one of the two devices.

This section is categorized into three parts. The first part is the experiment setup, where the hardware and its corresponding configurations used in the evaluation are introduced. In the second part, the experiment results for fixed reply times at different locations (LOS at a hall, a multipath scenario at the corridor in an office building, and close LOS less then 2 m) are expressed. The goal is to clarify the errors caused by the delays (PTD and PATD) as mentioned in Section3.1. In the third part, comparative analysis between three TWRs is conducted at a fixed location (distance) in the laboratory with varying reply times. The goal is to point out the pitfalls of the SDS-TWR method in a typical case, and to prove that AltDS-TWR holds stable results in each reply-time variation. The test environments where the experimental evaluations presented in this section were conducted are illustrated in Figure6.

(a) Floor plan of test environments (b) Measurement at 5.494m (lab.)

(c) LOS measurement at Hall (d) Multi-path at Corridor

NodeB NodeA NodeA

NodeB

NodeA

NodeB

Figure 6. Test environments of the experimental evaluations: (a) overview of office floor plan for the LOS experiment in hall (blue arrow) and the multipath experiment in a corridor (red arrow), (b) fixed-distance experiment in the laboratory, (c) LOS experiment in a hall (office environment), and (d) multipath experiment in a corridor (office environment).

7.1. Setup and Data-Collection Process for Experimental Evaluations

For experimental evaluations, we used a DWM1000 module [27] from Decawave as the UWB hardware, and an STM32 development board (NUCLEO-L476RG) from STMicroelectronics as the main microcontroller (MCU). Moreover, the built-in high-speed internal (HSI) clock source (16 MHz) from the MCU was applied to all of the evaluation results presented in this article. No external oscillators

were connected to the MCU. The HSI has an accuracy of±1 % using the factory-trimmed RC oscillator according to the datasheet [28].

Aggregated antenna delay calibration was conducted before measurement according to the procedure and algorithm provided by the manufacturer [29,30]. This aggregated antenna delay corresponds to transmission and receiving time delays (TTD and RTD) of the evaluated hardware described in Section3.1. Therefore, the remaining error that influences the accuracy of TOF error estimation in our measurement would be PTD and PATD. The results presented in Section7are the errors and their corresponding parameters in distance (not in TOF). This is because all of the references used in the experiment are measured in distance, which means that TOF value is already calculated as a distance by multiplying with the speed of light (299,702,547 m s⁻¹in air).

During measurement, one of the transceivers (Device A in Figure1) is connected to a computer for logging the data received from the MCU via serial USART port. Two-way ranging software, provided by Decawave for production testing of their evaluation kit (EVK1000), which is available online (https:

//www.decawave.com/software/) on Decawave’s website, was executed on the two transceivers.

The software was modified so that the four periods of time (troundA,troundB,treplyA, andtreplyB) were individually logged and saved into a file at each measurement. The above-mentioned time periods from the log file were afterward processed with the TWR formulas provided in Section2using Matlab.

This ensured that the same raw data (time periods) were used for the three TWRs in the evaluation. For instance, a subset of the four collected time periods, i.e.,troundAandtreplyB, was used to study SS-TWR.

All of the reference distances in the evaluation were measured with a laser distance meter, CEM iLDM-150 model (http://www.cem-instruments.in/product.php?pname=iLDM-150), which has an accuracy of±1.5 mm according to the manufacturer. The hardware configuration of the used UWB module in the experimental evaluations is described in Table3. Antenna height was 1.06 m in all the experiments reported in this paper. This ensured that the effect of Fresnel zones did not perturb measurement results.

Table 3.Used Ultrawide Bandwidth (UWB) configuration in the evaluations.

Properties Values

Data rate 6.8 Mbps

Channel 2

Center frequency 3993.6 MHz

Bandwidth 499.2 MHz

Pulse-repetition frequency (PRF) 16 MHz Preamble code sequence index [3] (p. 203) 3

Module name DWM1000

Manufacturer Decawave

Reported precision [27] 10 cm

For a symmetric condition in special cases (Type II), the hardware for the two transceivers was tuned until the two reply times were approximately equal (symmetric). The histogram of the sample data for symmetric replied time (special case, or Type II) collected from one of our measurements is shown in Figure7. The figure shows the measured time periods for a single trial conducted roughly around 5 min with an updated rate of 10 Hz. The mean values of the reply times aretreplyA =490.94 µs andt_replyB=491.25 µs (Figure7and Table4). This setting and reply time were used throughout all of the evaluation results presented in this paper for a symmetry case (Type II).

(a) Measured Data of t_replyA

4.90935 4.9094 4.90945 4.9095 4.90955 10^-4 0

20 40 60 80 100

(b) Measured Data of t_replyB

4.91245 4.9125 4.91255 4.9126 4.91265 10^-4 0

50 100 150

(c) Measured Data of t_roundA

4.913 4.91305 4.9131 4.91315 4.9132

Time / s 10^-4

0 50 100 150

(d) Measured Data of t_roundB

4.90985 4.9099 4.90995 4.91 4.91005

Time / s 10^-4

0 20 40 60 80 100

Figure 7.Measured data for fixed reply times used in the experiments for the special case (Type II) For an asymmetric condition in a typical case (Type III), the histogram of the sample data collected from one of our measurement is illustrated in Figure8. Again, the figure illustrates the measured time periods for a single trial. The mean values of the reply times aret_replyA =836.8 µs, and t_replyB=397.4 µs (Figure8and Table4). Note that this is the default setup (out of the box) achieved from the software provided by Decawave. This setting and reply times are used for the measurement conducted in LOS (hall), multipath (Corridor), and close LOS. However, reply time was varied on one device at each evaluation conducted in Section7.3to compare the performance difference between the SDS- and AltDS-TWR methods.

(a) Measured Data of t_replyA

8.355 8.36 8.365 8.37 8.375 8.38 10^-4 0

200 400 600

(b) Measured Data of t_replyB

3.96 3.965 3.97 3.975 3.98 3.985 10^-4 0

200 400 600

(c) Measured Data of t_roundA

3.96 3.965 3.97 3.975 3.98 3.985

Time / s 10^-4

0 200 400 600

(d) Measured Data of t_roundB

8.36 8.365 8.37 8.375 8.38

Time / s 10^-4

0 200 400 600

Figure 8.Measured data for fixed reply times used in the experiments for a typical case (Type III) Table4represents the sample data of reply times for Types II and III, which were randomly drawn from the measurement conducted in the three categories, at LOS, close LOS, and multipath

scenarios. It was confirmed that the magnitude of difference (similarity) between the two reply times (t_replyAandt_replyB), which is annotated as root mean square error (RMSE) in Table4, for the symmetry case (Type II) in all of our measurements was always less than 0.35 µs in average.

Table 4.Sample reply time drawn randomly from each of the three categories (LOS, close LOS, and multipath scenarios). Note: RMSE, Root Mean Square Error.

Cases RMSE (µs) Mean (µs) STD (ns) Data Spread (ns)

Sample Size (treplyA−treplyB) treplyA treplyB treplyA treplyB treplyA treplyB

Special case 0.31 490.94 491.25 2.29 2.32 8.17 8.00 2350

(Type II) 0.28 490.97 491.25 2.30 2.32 8.47 8.00 2450

0.26 491.0 491.25 2.34 2.34 9.14 8.00 2000

Typical case 439.41 836.80 397.40 357.14 357.11 1754.5 1754.0 2350

(Type III) 439.58 836.90 397.33 375.07 375.07 4451.3 4451.6 2450

439.83 837.04 397.22 1369.1 1369.1 16,474.0 16,474.0 2000

7.2. Comparative Analysis of Distance Errors in Fixed Reply Times at Different Scenarios

In this subsection, experimental evaluations of three scenarios, that is, close LOS, LOS (Hall), and multipath (Corridor), were conducted to validate the error influenced by the PTD and PATD. The effect of PTD can be seen in the multipath scenario, where measurement was conducted in the corridor of an office building (Section7.2.1), and in the Non-LOS (NLOS) scenario (Section7.3.2). In the same way, the effect of PATD can be seen in the close LOS scenario, where measurement was conducted within less than 2 m (Section7.2.2). The complete detailed report of the three scenarios is presented in Section7.2.3(see Table5for the special case (Type II) and Table6for the typical case (Type III)).

7.2.1. Distance Error Comparison for Types II and III at LOS and Multipath Scenarios

To evaluate the distance error caused by the effect of a multipath signal in TWR, measurement was conducted at different ranges for both an LOS scenario (Figure6c) where measurement was done in a big hall, and a multipath scenario (Figure6d) where measurement was conducted in the narrow corridor of an office environment. Note that the UWB signal natively overcomes the multipath effects compared to other narrow-band signals. However, signal disturbance because of multipath effects in UWB is still noticeable in distance error estimation, as is shown in the following paragraphs.

Figure9depicts the measurement results for the exact same distance (4 m) for two separate scenarios (LOS at hall and multipath at corridor). The first row, Figure9a–c, illustrates the results achieved from the LOS condition, and the second row, Figure9d–f, illustrates the results achieved from the multipath scenario.

Furthermore, the measured results for both Type II and III are compared side by side in Figure9 to clearly see the differentiation between the two cases. It can be seen in the experiment result that SDS and AltDS have approximately the same performance level in the special case (Type II) as already stated in the simulation results (Section6, see Figure9a,d). However, a significant variation between SDS and AltDS can be observed in the typical case (Type III) as expected from the simulation results (Section6, see Figure9b,e).

Regarding distance error in the TWR approach, it was observed that both SDS and AltDS outperformed SS-TWR with significant distinction in all cases (Figure9). Particularly for the LOS scenario (first row in Figure9), the measured distances of both SDS and AltDS were very close to the reference value in Type II (Figure9a). However, AltDS had the smallest error between the three in the typical case (Figure9b). In the multipath scenario (second row in Figure9), the distance error caused by SDS and AltDS was still small compared to that of SS-TWR in the special case (Figure9d), even though their errors were slightly higher compared with the LOS case (Figure9a,d). In the typical case (Type III), the figure suggests that SDS had the smallest error beetween the three methods (Figure9e).

This condition is further analyzed for clarity in Section7.3.

AltDS SDS SS -0.3

-0.25 -0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15

Distance variance / m

(a)LOS scenario for Type II at 4.00 / m

Ref.

AltDS SDS SS

-0.3 -0.25 -0.2 -0.15 -0.1 -0.05 0 0.05 0.1

0.15 (b) LOS scenario for Type III at 4.00 / m

Ref.

3.8 3.9 4 4.1 4.2 4.3

x 0

0.2 0.4 0.6 0.8 1

F(x)

(c) Empirical CDF for LOS at 4.00 / m

AltDS T2 AltDS T3 SDS T2 SDS T3 SS T2 SS T3 Ref.

AltDS SDS SS

-0.3 -0.25 -0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15

Distance variance / m

(d) Multi-path for Type II at 4.02 / m

Ref.

AltDS SDS SS

-0.3 -0.25 -0.2 -0.15 -0.1 -0.05 0 0.05 0.1

0.15 (e) Multi-path for Type III at 4.02 / m

Ref.

3.9 4 4.1 4.2 4.3 4.4

x 0

0.2 0.4 0.6 0.8 1

F(x)

(f) Empirical CDF for multipath at 4.02 / m

AltDS T2 AltDS T3 SDS T2 SDS T3 SS T2 SS T3 Ref.

Figure 9. Comparison of Type II and Type III for LOS and multipath scenarios at a 4 m true reference. (a–c) measured data from the LOS (Hall), and (d–f) measured data from the multipath (Corridor) scenario.

In general, the multipath effect caused a big data shift in all of the measurements for all three of the evaluated methods. This shift can clearly be seen by comparing the empirical cumulative distribution function (eCDF) for the LOS scenario, presented in Figure9c, and for the multipath scenario, presented in Figure9f. This corresponds to the contribution of the delay caused by the multipath signal in distance or TOF error estimation as stated in Section3.1. This delay could be the PTD because of the reflection of the signal as well as the PATD in the case of multiple signals arriving within the chip period of the first path signal, as described in Section3.1.

Figure9gives inside knowledge for visualizing the experimental data for the two scenarios (LOS and multipath), specifically measured at true reference 4 m. The complete dataset for Types II and III at different ranges in two scenarios (LOS and multipath) is provided in Figure10. The data in Figure10 represent the RMSE, which is the square root of the mean error between the measurement and the true reference of the special and typical cases (Types II and III) for the three evaluated TWR (AltDS, SDS, and SS) at different locations in two scenarios (LOS and multipath).

In general, it was observed that the distance error for AltDS was less than 6.43 cm in all of the measurements at both the special case (Type II) and the typical case (Type III) (see the first two columns in Figure10). Moreover, the measured distance error for all locations in AltDS and SDS was approximately equal in the special case (Type II) (see the first and third columns in Figure10).

Obviously, the largest distance errors in the measurement occurred in SS-TWR (Figure10).

In the multipath scenario at Type III (esp. 4, 8, and 12 m), the figure suggests that the distance error in SDS provides the smallest among the three evaluated methods (the fourth column in Figure10).

This happens because of the chosen fixed reply time (t_replyA =836.8 µs andt_replyB =397.4 µs) for a typical case in this particular multipath condition. The issue is further clarified by varying the reply time of one device using different values in the measurement (see Section7.3).

Figure 10.Measured distance error comparison of Types II and III for three TWRs evaluated in different locations in LOS and multipath scenarios

7.2.2. Distance Error Comparison for Types II and III at a Close LOS Scenario

To evaluate the PATD effect, measurement for close LOS (measured distances range from 0.25 up to 2 m) was conducted at one of the CITEC laboratories, Bielefeld University (Figure6b).

PATD occurrence is significant in close LOS, especially when a coherent receiver architecture is used in the hardware [22]. The reason is that a sequence of preamble code is necessary to synchronize in the physical layer before data communication between transceivers can be started using the property of perfect periodic autocorrelation [3,22]. Moreover, most of the commercially available UWB hardware modules, including DWM1000, used in this evaluation are based on a coherent receiver structure. In this experiment evaluation, preamble sequence code index no. 3 was used, which has the code sequence pattern of “−+0+ +000−+−+ +00+ +0+00−0000−0+0−” according to References [3,22] (p. 203). This sequence is regarded as a short one in UWB configurations. It is expected that, the longer the code sequence is, the more likely to have severe error in close LOS measurement. The reason is that the base symbol rate for the synchronization header is proportional to the preamble symbol transmission rate [3] (pp. 200–207). This means that the longer the preamble length is, the longer it takes to detect the start of frame delimiter (SFD) during accumulation time.

Regarding this, data visualization using boxplots for Types II and III at a true reference of 0.5, 1.0, and 1.5 m is presented in Figure11. The RMSE regarding measured distance error for the three evaluated TWRs in Types II and III, conducted at close LOS, is provided in Figure12.

AltDS SDS SS -0.2

-0.1 0 0.1 0.2 0.3 0.4 0.5

Distance variance / m

(a) Type II at 0.501 / m

Ref.

AltDS SDS SS

-0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5

(b) Type II at 1.039 / m

Ref.

AltDS SDS SS

-0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5

(c) Type II at 1.503 / m

Ref.

AltDS SDS SS

-0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5

Distance variance / m

(d) Type III at 0.501 / m

Ref.

AltDS SDS SS

-0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5

(e) Type III at 1.039 / m

Ref.

AltDS SDS SS

-0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5

(f) Type III at 1.503 / m

Ref.

Figure 11. Results comparison of Types II and III for close LOS at true reference 0.25, 1.00, and 1.50 m. (a–c) measurement results for Type II (special case), and (d–f) corresponding results for Type III (typical case).

Figure 12.Measured distance error (RMSE) comparison of Types II and III for three TWRs in a close LOS scenario.

In general, a significantly high rate of outliers (symbolized with red plus signs) is presented in the data of measurement results less than 0.75 m (see the sample data measured at 0.5 m (Figure11a,d).